Risk Analysis. Two-Stock Portfolios. Adding Stocks to a Portfolio. The Capital Asset Pricing Model

Transcription

1 Risk Analysis The Capital Asset Pricing Model 1 Two-Stock Portfolios Two stocks can be combined to form a riskless portfolio if = Risk is not reduced at all if the two stocks have = In general, stocks have 0.35, so risk is lowered but not eliminated. Investors typically hold many stocks. What happens when = 0? 2 Adding Stocks to a Portfolio What would happen to the risk of an average 1-stock portfolio as more randomly selected stocks were added? p would decrease because the added stocks would not be perfectly correlated, but the expected portfolio return would remain relatively constant. 3

2 stock 35% Many stocks 20% 1 stock 2 stocks Many stocks Returns (%) 4 Risk vs. Number of Stock in Portfolio 35% p Company Specific (Diversifiable) Risk Stand-Alone Risk, p 20% Market Risk ,000 stocks5 Stand-alone risk = Market risk + Diversifiable risk Market risk is that part of a security s stand-alone risk that cannot be eliminated by diversification. Firm-specific, or diversifiable, risk is that part of a security s stand-alone risk that can be eliminated by diversification. 6

3 Conclusions As more stocks are added, each new stock has a smaller risk-reducing impact on the portfolio. p falls very slowly after about 40 stocks are included. The lower limit for p is about 20%= M. By forming well-diversified portfolios, investors can eliminate about half the risk of owning a single stock. 7 Can an investor holding one stock earn a return commensurate with its risk? No. Rational investors will minimize risk by holding portfolios. They bear only market risk, so prices and returns reflect this lower risk. The one-stock investor bears higher (stand-alone) risk, so the return is less than that required by the risk. 8 How is market risk measured for individual securities? Market risk, which is relevant for stocks held in well-diversified portfolios, is defined as the contribution of a security to the overall riskiness of the portfolio. It is measured by a stock s beta coefficient. For stock i, its beta is: b i = ( i,m i ) / M 9

4 How are betas calculated? In addition to measuring a stock s contribution of risk to a portfolio, beta also which measures the stock s volatility relative to the market. 10 Use the historical stock returns to calculate the beta for PQU. Year Market PQU % 40.0% 2 8.0% -15.0% % -15.0% % 35.0% % 10.0% % 30.0% % 42.0% % -10.0% % -25.0% % 25.0% 11 Calculating Beta for PQU PQU Return 50% 40% 30% 20% 10% 0% -10% -20% -30% r PQU = r M R 2 = % -20% -10% 0% 10% 20% 30% 40% 50% Market Return 12

5 What is beta for PQU? The regression line, and hence beta, can be found using a calculator with a regression function or a spreadsheet program. In this example, b = Calculating Beta in Practice Many analysts use the S&P 500 to find the market return. Analysts typically use four or five years of monthly returns to establish the regression line. Some analysts use 52 weeks of weekly returns. 14 How is beta interpreted? If b = 1.0, stock has average risk. If b > 1.0, stock is riskier than average. If b < 1.0, stock is less risky than average. Most stocks have betas in the range of 0.5 to 1.5. Can a stock have a negative beta? 15

6 Finding Beta Estimates on the Web Go to Thomson ONE Business School Edition using the information on the card that comes with your book. Enter the ticker symbol for a Stock Quote, such as IBM or Dell, then click GO. 16 Other Web Sites for Beta Go to Enter the ticker symbol for a Stock Quote, such as IBM or Dell, then click GO. When the quote comes up, select Key Statistics from panel on left. 17 Expected Return versus Market Risk: Which investment is best? Security Expected Return (%) Risk, b Alta Market Am. Foam T-bills Repo Men

7 Use the SML to calculate each alternative s required return. The Security Market Line (SML) is part of the Capital Asset Pricing Model (CAPM). SML: r i = r RF + (RP M )b i. Assume r RF = 8%; r M = r M = 15%. RP M = (r M -r RF ) = 15% - 8% = 7%. 19 Required Rates of Return r Alta = 8.0% + (7%)(1.29) = 17%. r M = 8.0% + (7%)(1.00) = 15.0%. r Am. F. = 8.0% + (7%)(0.68) = 12.8%. r T-bill = 8.0% + (7%)(0.00) = 8.0%. r Repo = 8.0% + (7%)(-0.86) = 2.0%. 20 Expected versus Required Returns (%) Exp. Req. r r Alta Undervalued Market Fairly valued Am. F Undervalued T-bills Fairly valued Repo Overvalued 21

8 SML: r i = r RF + (RP M ) b i r i = 8% + (7%) b i r i (%) r M = 15. Alta. r Am. Foam RF = 8 T-bills Repo Market Risk, b i 22 Calculate beta for a portfolio with 50% Alta and 50% Repo b p = Weighted average = 0.5(b Alta ) + 0.5(b Repo ) = 0.5(1.29) + 0.5(-0.86) = Required Return on the Alta/Repo Portfolio? r p = Weighted average r = 0.5(17%) + 0.5(2%) = 9.5%. Or use SML: r p = r RF + (RP M ) b p = 8.0% + 7%(0.22) = 9.5%. 24

9 Has the CAPM been completely confirmed or refuted? No. The statistical tests have problems that make empirical verification or rejection virtually impossible. Investors required returns are based on future risk, but betas are calculated with historical data. Investors may be concerned about both stand-alone and market risk. 25